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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improvement and generalization of ABCD method with Bayesian inference

To find New Physics or to refine our knowledge of the Standard Model at the LHC is an enterprise that involves many factors, such as the capabilities and the performance of the accelerator and detectors, the use and exploitation of the available information, the design of search strategies and observables, as well as the proposal of new models. We focus on the use of the information and pour our effort in re-thinking the usual data-driven ABCD method to improve it and to generalize it using Bayesian Machine Learning techniques and tools. We propose that a dataset consisting of a signal and many backgrounds is well described through a mixture model. Signal, backgrounds and their relative fractions in the sample can be well extracted by exploiting the prior knowledge and the dependence between the different observables at the event-by-event level with Bayesian tools. We show how, in contrast to the ABCD method, one can take advantage of understanding some properties of the different backgrounds and of having more than two independent observables to measure in each event. In addition, instead of regions defined through hard cuts, the Bayesian framework uses the information of continuous distribution to obtain soft-assignments of the events which are statistically more robust. To compare both methods we use a toy problem inspired by pp\to hh\to b\bar b b \bar b p p → h h → b b ‾ b b ‾ , selecting a reduced and simplified number of processes and analysing the flavor of the four jets and the invariant mass of the jet-pairs, modeled with simplified distributions. Taking advantage of all this information, and starting from a combination of biased and agnostic priors, leads us to a very good posterior once we use the Bayesian framework to exploit the data and the mutual information of the observables at the event-by-event level. We show how, in this simplified model, the Bayesian framework outperforms the ABCD method sensitivity in obtaining the signal fraction in scenarios with 1% and 0.5% true signal fractions in the dataset. We also show that the method is robust against the absence of signal. We discuss potential prospects for taking this Bayesian data-driven paradigm into more realistic scenarios.

Alvarez, Ezequiel↗
DOE OSTI2023

Low Energy Analysis of NuclEar Reactions v0.0.1

This is a lightweight, easy to use Python analysis package for analyzing public low-energy nuclear reaction data relevant to understanding basic nuclear processes, often of relevance to Solar Fusion, to improve our theoretical understanding of them, and enable connections with input from lattice QCD. It performs the analysis in a Bayesian Framework and supports Bayesian Model Averaging to provide a robust uncertainty quantification.

Walker-Loud, André↗
NASA NTRS2018

Exoplanet Biosignatures: At the Dawn of a New Era of Planetary Observations

The rapid rate of discoveries of exoplanets has expanded the scope of the science possible for the remote detection of life beyond Earth. The Exoplanet Biosignatures Workshop-Without-Walls (EBWWW) held in 2016 engaged the international scientific community across diverse scientific disciplines, to assess the state of the science and technology in the search for life on exoplanets, and to identify paths for progress. The workshop activities resulted in five (5) major review papers which provide: 1) an encyclopedic review of known and proposed biosignatures and models used to ascertain them; 2) an in-depth review of O2 as a biosignature, rigorously examining the nuances of false positives and negatives for evidence of life; 3) a Bayesian framework to comprehensively organize current understanding to quantify confidence in biosignature assessments; 4) an extension of that Bayesian framework in anticipation of increasing planetary data and novel concepts of biosignatures, and 5) a review of the upcoming telescope capabilities to characterize exoplanets and their environment. Because of the immense content of these review papers, this summary provides a guide to their complementary scope and highlights salient features. Strong themes that emerged from the workshop were that biosignatures must be interpreted in the context of their environment, and that frameworks must be developed to link diverse forms of scientific understanding of that context to quantify the likelihood that a biosignature has been observed. Models are needed to explore the parameter space where measurements will be widespread but sparse in detail. Given the technological prospects for large ground-based telescopes and direct imaging from space-based observatories, the detection of atmospheric signatures of a few potentially habitable planets may come before 2030.

spectral imaging↗
DOE OSTI2024

Bayesian Fit for the NOvA Three Flavor Oscillation Analysis

NOvA is a long baseline neutrino oscillation experiment, using Fermilab's NuMI beam and a functionally identical near and far detector. NOvA measures muon neutrino disappearance and electron neutrino appearance to probe neutrino oscillation parameters, including the large neutrino mixing angle, the mass ordering, and the CP-violating phase. NOvA has developed a Bayesian analysis in addition to its Frequentist analysis, using Markov Chain Monte Carlo. This Bayesian framework allows for measurements previously difficult to make with the Frequentist framework, such as the Jarlskog invariant and the reactor mixing angle. The details and status of the Bayesian Framework will be presented, as well as latest NOvA results on measurements of three-flavor oscillation parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2009

Development of an On-board Failure Diagnostics and Prognostics System for Solid Rocket Booster

We develop a case breach model for the on-board fault diagnostics and prognostics system for subscale solid-rocket boosters (SRBs). The model development was motivated by recent ground firing tests, in which a deviation of measured time-traces from the predicted time-series was observed. A modified model takes into account the nozzle ablation, including the effect of roughness of the nozzle surface, the geometry of the fault, and erosion and burning of the walls of the hole in the metal case. The derived low-dimensional performance model (LDPM) of the fault can reproduce the observed time-series data very well. To verify the performance of the LDPM we build a FLUENT model of the case breach fault and demonstrate a good agreement between theoretical predictions based on the analytical solution of the model equations and the results of the FLUENT simulations. We then incorporate the derived LDPM into an inferential Bayesian framework and verify performance of the Bayesian algorithm for the diagnostics and prognostics of the case breach fault. It is shown that the obtained LDPM allows one to track parameters of the SRB during the flight in real time, to diagnose case breach fault, and to predict its values in the future. The application of the method to fault diagnostics and prognostics (FD&P) of other SRB faults modes is discussed.

Smelyanskiy, Vadim N.↗
DOE OSTI2025

Simultaneous inference of equation of state parameters and unknown data errors with uncertainty quantification via hierarchical Bayesian posterior maximization

Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

A Framework for Inferring Taxonomic Class of Asteroids.

Introduction: Taxonomic classification of asteroids based on their visible / near-infrared spectra or multi band photometry has proven to be a useful tool to infer other properties about asteroids. Meteorite analogs have been identified for several taxonomic classes, permitting detailed inference about asteroid composition. Trends have been identified between taxonomy and measured asteroid density. Thanks to NEOWise (Near-Earth-Object Wide-field Infrared Survey Explorer) and Spitzer (Spitzer Space Telescope), approximately twice as many asteroids have measured albedos than the number with taxonomic classifications. (If one only considers spectroscopically determined classifications, the ratio is greater than 40.) We present a Bayesian framework that provides probabilistic estimates of the taxonomic class of an asteroid based on its albedo. Although probabilistic estimates of taxonomic classes are not a replacement for spectroscopic or photometric determinations, they can be a useful tool for identifying objects for further study or for asteroid threat assessment models. Inputs and Framework: The framework relies upon two inputs: the expected fraction of each taxonomic class in the population and the albedo distribution of each class. Luckily, numerous authors have addressed both of these questions. For example, the taxonomic distribution by number, surface area and mass of the main belt has been estimated and a diameter limited estimate of fractional abundances of the near earth asteroid population was made. Similarly, the albedo distributions for taxonomic classes have been estimated for the combined main belt and NEA (Near Earth Asteroid) populations in different taxonomic systems and for the NEA population specifically. The framework utilizes a Bayesian inference appropriate for categorical data. The population fractions provide the prior while the albedo distributions allow calculation of the likelihood an albedo measurement is consistent with a given taxonomic class. These inputs allows calculation of the probability an asteroid with a specified albedo belongs to any given taxonomic class.

Asteroids↗
DOE OSTI2024

Thermodynamically informed priors for uncertainty propagation in first-principles statistical mechanics

Here, this work demonstrates how first-principles statistical mechanics approaches within a Bayesian framework can quantify and propagate uncertainties to downstream thermodynamic calculations. To address the issue of Bayesian prior selection, knowledge of 0 K ground states in the material system of interest is incorporated into the prior. The effectiveness of this framework is shown by creating a phase diagram for the fcc zirconium nitride system, including confidence intervals on order-disorder transition temperatures.

Bayesian methods↗
DOE OSTI2022

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Gaussian processes for inferring parton distributions

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.

hadronic spectroscopy↗
DOE OSTI2023

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗
DOE OSTI2024

Assay-based background projection for the Majorana Demonstrator using Monte Carlo uncertainty propagation

The background index (BI) is an important quantity to project and calculate the half-life sensitivity of neutrinoless double-𝛽 decay (0⁢𝜈⁢𝛽⁢𝛽) experiments. An analysis framework is presented to calculate the BI using the specific activities, masses, and simulated efficiencies of an experiments components as distributions. This Bayesian framework includes a unified approach to combine specific activities from assay. Monte Carlo uncertainty propagation is used to build a BI distribution from the specific activity, mass, and efficiency distributions. This method is applied to the M AJORANA D EMONSTRATOR , which deployed arrays of high-purity Ge detectors enriched in 76 Ge to search for 0⁢𝜈⁢𝛽⁢𝛽. The original assay-based projection is requantified in the new framework, using the as-built geometry of the Demonstrator and additional assay information. While 47% higher than the original projection, the resulting BI of [8.95±0.36]×10 −4 cts/(keVkgyr) from the 232 Th and 238 U decay chains does not account for the higher-than-expected BI observed by the D EMONSTRATOR . Finally, this method enables us to demonstrate the statistical incompatibility between the D EMONSTRATOR 's observed background and the assay results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Bayesian D‐Optimal Designs for Gaussian Process Surrogate Models

Computer experiments often employ space-filling strategies to create surrogate models with strong predictive performance. The impact of model parameter estimation for Gaussian process surrogates, however, is often overlooked. Obtaining a better initial estimate of the covariance lengthscale parameter, θ, can greatly improve the resulting Gaussian process fit through more effective sequential acquisitions during active learning. In this work, we propose a novel initial design maximizing the Bayesian D-optimality criterion of the Gaussian process lengthscale parameter. Previously published results have shown the emphasis on lengthscale estimation to be promising, but relied on an empirically driven design creation process. Our Bayesian D-optimal designs are rooted in information theory and lead to more informative sequential acquisitions by improving lengthscale estimation. In many cases, these gains eventually result in better surrogates than those seeded with space-filling initial designs. Furthermore, Bayesian D-optimal designs can be tailored to either isotropic or anisotropic covariance structures, and the Bayesian framework enables the inclusion of prior knowledge in the design process, offering greater flexibility and adaptability. Through several simulation studies, we demonstrate the advantages of Bayesian D-optimal designs in terms of both lengthscale estimation accuracy and predictive performance during active learning.

Bayesian experimental design↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗